Which equation represents the simplified form of the law of conservation of energy during the block's motion from the table to the ramp?

The law of conservation of energy states that the total energy in a closed system remains constant over time. In the context of a block moving from a table to a ramp, we consider the initial kinetic energy and gravitational potential energy at the top, and the final kinetic energy and gravitational potential energy at the bottom.

The initial state consists of kinetic energy, represented as ( \frac{1}{2} mv_i^2 ), where ( m ) is the mass of the block and ( v_i ) is its initial velocity, plus gravitational potential energy given by ( mgh_i ), where ( h_i ) is the initial height of the block. As the block moves down to the ramp, this energy transforms into two forms: kinetic energy at the bottom, ( \frac{1}{2} mv_f^2 ), where ( v_f ) is the final velocity, and some gravitational potential energy, ( mgh_f ), at the height ( h_f ).

The equation ( \frac{1}{2} mv_i^2 + mgh_i = \frac{1}{2} mv_f^2 + mgh_f ) accurately illustrates this transformation, showing that the sum of the initial kinetic and